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American Journal of Physics

From measuring electron charge to exploring particle-wave duality: A new didactic experimental approach

Evelyne Salançon, Alain Degiovanni, Laurent Lapena, Roger Morin

Published Feb 19, 2019• 1 citation
Publisher

Abstract

This paper points out the strong didactic potential of an experiment originally intended for electron source research. Using a dual stage micro-channel plate in a low-energy electron point projection microscope, electrons are spatially detected one by one. Field electron emission affords wide-ranging intensity, enabling the electron charge to be determined by comparing counting and analog measurements. The same setup is used to illustrate the buildup of an interference pattern from separate low-energy electron detection, thereby enabling the Planck constant to be determined. Both granular and continuous signals are directly observable in this educational approach.

DOI
10.1119/1.5086392

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This paper points out the strong didactic potential of an experiment originally intended for electron source research. Using a dual stage micro-channel plate in a low-energy electron point projection microscope, electrons are spatially detected one by one. Field electron emission affords wide-ranging intensity, enabling the electron charge to be determined by comparing counting and analog measurements. The same setup is used to illustrate the buildup of an interference pattern from separate low-energy electron detection, thereby enabling the Planck constant to be determined. Both granular and continuous signals are directly observable in this educational approach.
The study of the dual nature of the electron is proposed, with alterations in initial double-slit experiment. We are aware of mysterious nature of the quantum particles, particularly electrons. The particle behaves as wave, but upon observation, the wave-function of the electron is collapsed. No longer is an interference pattern observed, which in a sense, limits us and binds us to what we can measure and what we cannot, with current detection methods. In the double slit experiment, a source of high-intensity light is used to measure the position of the electrons, which leads to the collapse of the wave-function. An investigation is proposed to observe the effects of the low-intensity electric field on the duality of electron.
A primary electron beam of a transmission electron microscope is scattered into secondary beams by the planes of atoms of a single crystal. These secondary beams are focused to form a diffraction pattern on the final screen. This experiment is similar to the Thompson one which, independently by Davisson and Germer, demonstrated the de Broglie hypothesis of the existence of electron waves. Without changing the experimental apparatus, it is possible to realize an interference experiment with electrons coming from two spatially separated sources in analogy with the optical Young set-up. Both experiments are clear evidence of the electron wave-like behaviour. By varying the conditions of illumination, changes of the fringe visibility which reveal the spatial coherence properties of the electron beam, are displayed.
The Young-Feynman two-hole interferometer is widely used to present the electron wave-particle duality and in particular the buildup of interference fringes with single electrons. The teaching approach consists of two steps: i) electrons come through only one hole but diffraction effects are disregarded; ii) electrons come through both holes and interference fringes are described. Therefore, a student might believe that wave phenomena are not revealable in case i) but they arise only by the combined effect of electrons from the two holes. To avoid misunderstanding regarding the distribution of electrons passing through one hole, Fresnel and Fraunhofer diffraction patterns are discussed. In particular, an original experiment, realized with a standard electron microscope and a sample with round holes is presented to introduce the wave nature of electrons. The experimental results clearly show that a careful discussion of electron diffraction phenomena from one hole provides students with the evidence that the interference experiment from both holes is not strictly required to show the superposition of electron waves.
In the early 1900s more and more experimental evidence was accumulated indicating that microscopic particles show wave-like properties in certain situations. These particle-wave features are very evident, e.g., in measurements where electrons are diffracted from a double slit to propagate toward a screen where they are detected. Based on the classical averaging of particles discussed in Section 1.2.2, one expects that the double slit only modulates the overall intensity, not the spatial distribution. Experimentally, however, one observes a nearly perfect interference pattern at the screen implying that the electrons exhibit wave averaging features such as discussed in Section 2.1.2. This behavior, originally unexpected for particle beams, persists even if the experiment is repeated such that only one electron at a time passes the double slit before it propagates to the detection screen. Thus, the wave aspect must be an inherent property of individual electrons and not an ensemble effect. Another, independent argument for the failure of classical physics is that the electromagnetic analysis of atoms leads to the conclusion that the negatively charged electron(s) should collapse into the positively charged ion because the electron–ion system loses its energy due to the emission of radiation. As we will see, this problem can be solved by including the wave aspects of particles into the analysis. In particular, as discussed in Section 2.3.3, waves can never be localized to a point without increasing their momentum and energy beyond bounds.